A matrix game without a pure strategy equilibrium

Question

I would like to see a matrix $2\times 2$ game without a pure strategy Nash equilibrium.

Answer 1

\begin{array}{|c|c|} \hline & H & T \\ \hline H & (1, 0) & (0, 1) \\ \hline T & (0, 1) & (1, 0) \\ \hline \end{array}

There is no Nash equilibrium in pure strategies, but there exists a Nash equilibrium in mixed strategies, both players choose H with probability $\frac{1}{2}$ and T with probability $\frac{1}{2}$.